Mike,
I worked in NYPD APD for a short period of time. I am a NY'er and do not sugar coat anything. If I come off offensive, its who I am not and not personal. With that said, you are an automatic DQ with the NYPD.
The NYPD looks at arrests, not convictions. I won't get into why or the what, but its the way it works. There is usually more truth in a the arresting charge than what a court pleas it down to. The NYPD policy is clear, one misdemeanor arrest may be "waived," if such was for a non-drug offense. You have three, and one is a drug charge. The DC or OC may have been a summons to criminal court, however a summons to criminal court in NYC is always "in liu of arrest." Meaning the street cop cut you some slack and made a judgement call.
Additionally, you driving skills are very carefully reviewed at the NYPD. The NYPD has had problems with off-duty cops and DWI. They also have liability issues with cops driving like maniacs in the city and not following the rules. The rule is "If they can't drive safe on their own time when they are not a cop, they definatley won't do so with our badge." They don't care what the charges are (unless DUI/DWI), just number of tickets. The brass of thw NYPD beliwve in "Once a ______, always a ______."
It is worth a try to make yourself feel better. But I would seriously come up with a back-up plan. The way it will work is you will: meet your BI; pay the city $ to run your prints; have a written psych; do a medical; have oral psych where you will get grilled and never hear from the NYPD again. No letter, no call. Your inquiry will be met with "you are on a psych hold." You will stay there till your exam expires. The NYPD has a pool of canidates with clean backgrounds and veterans preference. The current pool of canidates is around 23,000. And each year they MAY hire two classes, ranging from 500 to 1,500.
-In God we trust. All others, put your hands on the car and don't move.